I enjoy crime and political thrillers, but came across an interesting difference in facts between the last two I read.
Both involved threats against the US president, and both have sections from the Secret Service point of view. But the first one I read goes in to great detail that the president is not warned of any specific threat, (itís a significant plot point), yet the next book had him told immediately.
Is there any publicly known policy about this.

Given that the Secret Service probably deals with dozens of "plots" on a daily basis, I would not find this unrealistic at all.

I suppose that if they did have near concrete information, they might inform the President. But, I would also suppose that if they did inform the President, they would take other means to protect him (eg, change schedule, method of travel, route etc)

Who would like to be President and hear daily the plots on their life?

I'm not sure we can know the answer because I don't think the Secret Service would publicly comment on it. Although I guess one side of it could be disproved if a President (a trustworthy one, I mean) reported being told of a specific threat.

I do know that Secret Service protection is sometimes extended to more that the normally protected people at the President's discretion. I would think that might sometimes be sought based on specific threats. So, at least as to other people, I would think that Presidents are sometimes briefed on specific threats, but I don't know for sure.